The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory

Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for improving the convergence are discussed when the R-function series is truncated for practical applications.Comment: 16 pages, Late

Convergence of expansions in Schr\"odinger and Dirac eigenfunctions, with an application to the R-matrix theory

Expansion of a wave function in a basis of eigenfunctions of a differential eigenvalue problem lies at the heart of the R-matrix methods for both the Schr\"odinger and Dirac particles. A central issue that should be carefully analyzed when functional series are applied is their convergence. In the present paper, we study the properties of the eigenfunction expansions appearing in nonrelativistic and relativistic $R$-matrix theories. In particular, we confirm the findings of Rosenthal [J. Phys. G: Nucl. Phys. 13, 491 (1987)] and Szmytkowski and Hinze [J. Phys. B: At. Mol. Opt. Phys. 29, 761 (1996); J. Phys. A: Math. Gen. 29, 6125 (1996)] that in the most popular formulation of the R-matrix theory for Dirac particles, the functional series fails to converge to a claimed limit.Comment: Revised version, accepted for publication in Journal of Mathematical Physics, 21 pages, 1 figur

Relativistic coupled-cluster single-double calculations of positron-atom bound states

Relativistic coupled-cluster single-double approximation is used to calculate positron-atom bound states. The method is tested on closed-shell atoms such as Be, Mg, Ca, Zn, Cd, and Hg where a number of accurate calculations is available. It is then used to calculate positron binding energies for a range of open-shell transition metal atoms from Sc to Cu, from Y to Pd, and from Lu to Pt. These systems possess Feshbach resonances, which can be used to search for positron-atom binding experimentally through resonant annihilation or scattering.Comment: submitted to Phys. Rev.

Elastic positron-cadmium scattering at low energies

The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at 2.2 eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the e+-Cd system. The s-wave binding energy is estimated to be 126±42 meV, with a scattering length of Ascat=(14.2±2.1)a0, while the threshold annihilation parameter, Zeff, was 93.9±26.5. The p-wave phase shift exhibits a weak shape resonance that results in a peak Zeff of 91±17 at a collision energy of about 490±50 meV

Calculation of the positron bound state with the copper atom

A new relativistic method for calculation of positron binding to atoms is presented. The method combines a configuration interaction treatment of the valence electron and the positron with a many-body perturbation theory description of their interaction with the atomic core. We apply this method to positron binding by the copper atom and obtain the binding energy of 170 meV (+ - 10%). To check the accuracy of the method we use a similar approach to calculate the negative copper ion. The calculated electron affinity is 1.218 eV, in good agreement with the experimental value of 1.236 eV. The problem of convergence of positron-atom bound state calculations is investigated, and means to improve it are discussed. The relativistic character of the method and its satisfactory convergence make it a suitable tool for heavier atoms.Comment: 15 pages, 5 figures, RevTe

Effective potentials for atom-atom interaction at low temperatures

We discuss the concept and design of effective atom-atom potentials that accurately describe any physical processes involving only states around the threshold. The existence of such potentials gives hope to a quantitative, and systematic, understanding of quantum few-atom and quantum many-atom systems at relatively low temperatures.Comment: 4 pages, 4 figure

The variable phase method used to calculate and correct scattering lengths

It is shown that the scattering length can be obtained by solving a Riccati equation derived from variable phase theory. Two methods of solving it are presented. The equation is used to predict how long-range interactions influence the scattering length, and upper and lower bounds on the scattering length are determined. The predictions are compared with others and it is shown how they may be obtained from secular perturbation theory.Comment: 7 pages including 3 figure

Supersymmetry and the relationship between a class of singular potentials in arbitrary dimensions

The eigenvalues of the potentials $V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^ {6}}$, and of the special cases of these potentials such as the Kratzer and Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The explicit dependence of these potentials in higher-dimensional space is discussed, which have not been previously covered.Comment: 13 pages article in LaTEX (uses standard article.sty). Please check "http://www1.gantep.edu.tr/~ozer" for other studies of Nuclear Physics Group at University of Gaziante

Theory and applications of atomic and ionic polarizabilities

Atomic polarization phenomena impinge upon a number of areas and processes in physics. The dielectric constant and refractive index of any gas are examples of macroscopic properties that are largely determined by the dipole polarizability. When it comes to microscopic phenomena, the existence of alkaline-earth anions and the recently discovered ability of positrons to bind to many atoms are predominantly due to the polarization interaction. An imperfect knowledge of atomic polarizabilities is presently looming as the largest source of uncertainty in the new generation of optical frequency standards. Accurate polarizabilities for the group I and II atoms and ions of the periodic table have recently become available by a variety of techniques. These include refined many-body perturbation theory and coupled-cluster calculations sometimes combined with precise experimental data for selected transitions, microwave spectroscopy of Rydberg atoms and ions, refractive index measurements in microwave cavities, ab initio calculations of atomic structures using explicitly correlated wave functions, interferometry with atom beams, and velocity changes of laser cooled atoms induced by an electric field. This review examines existing theoretical methods of determining atomic and ionic polarizabilities, and discusses their relevance to various applications with particular emphasis on cold-atom physics and the metrology of atomic frequency standards.Comment: Review paper, 44 page